October 30, 2018
Mr. WONG Ka Ho Department of Earth Sciences, HKU
Mean-motion resonance (MMR) is a resonance between two orbits that have near integer period ratio such that they have periodic conjunctions. MMRs appear in the rings of Saturn, to Galilean satellites, to asteroids and to exoplanets, and is important in their formation and architecture. MMRs between 2 bodies are referred to as 2-body resonances, and they have are extensively studied by previous authors. However in planetary systems of 3 or more planets, 3-body resonance/Laplace resonance can emerge, and such 3-body resonance is not a direct generalization of the 2-body case. Numerical and analytic understanding of 3-body is still lacking. Observationally, we have now detected 5 such systems, the most famous Trappist-1 have 7 planets in chain of 3-body resonances. using Trappist-1 as an example, we will show that 3-body resonance does not uniquely determine the dynamical state of a system, but can be divided into 3 or more distinct states. Planetary migration has strong preference to only 1 of these states but observation shows that Trappist-1 system could be in the other 2 states. We will discuss and explain the difference between these states. In the future we require more analytic and numerical work to quantitatively formalize these different states, and the possible way nature could assemble these different states.